QQuestion
If 1701 is the nth term of the Geometric Progression 7, 21, 63, …, find:
(a) the value of n.
(b) hence, the sum of the n terms of the G.P.
✓Answer
First term, a = 7
Common ratio, r = 21 ÷ 7 = 3
(a) The nth term of a G.P. is Tₙ = arⁿ⁻¹.
⇒ 1701 = 7 × 3ⁿ⁻¹
⇒ 3ⁿ⁻¹ = 1701 ÷ 7
⇒ 3ⁿ⁻¹ = 243
⇒ 3ⁿ⁻¹ = 3⁵
⇒ n − 1 = 5
⇒ n = 6
(b) Sum of n terms of a G.P. = \mathrm{S}_{\mathrm{n}}=\frac{\mathrm{a}(\mathrm{r}^{\mathrm{n}}-1)}{\mathrm{r}-1}
\mathrm{S}_6=\frac{7(3^6-1)}{3-1}= \frac{7(729-1)}{2}
= \frac{7\times728}{2}
= 7 × 364
= 2548
Therefore, n = 6 and the sum of the first six terms is 2548.
Related Questions
More ICSE Moderate level questions
The first term of an Arithmetic Progression is 5, the last term is 50 and the sum is 440. Find: (a) the number of terms. (b) the common difference.
Using graph paper, draw a histogram for the following distribution of marks obtained by 164 students and hence find the mode. Take 2 cm = 10 marks on one axis and 2 cm = 10 students on the other. Marks Number of students 30–40 10 40–50 26 50–60 40 60–70 54 70–80 34
The nth term of an Arithmetic Progression (A.P.) is given by the relation Tn = 6(7 − n). Find: (a) its first term and common difference. (b) the sum of its first 25 terms.
15, 30, 60, 120, ... are in G.P. (a) Find the nth term of this G.P. in terms of n. (b) How many terms of the above G.P. will give the sum 945?
The 5th term and the 9th term of an Arithmetic Progression are 4 and −12 respectively. Find: (a) the first term (b) the common difference (c) the sum of 16 terms of the A.P.
Refer to the bill below. A customer paid ₹2,000, rounded to the nearest ₹10, to clear it. Note: A 5% discount applies to an article when 10 or more units are purchased. Article Marked price Quantity GST A ₹190 6 12% B ₹50 12 18% Check whether the amount paid is correct. Justify your answer with working.
The given graph represents the monthly salaries, in rupees, of workers of a factory. Using the graph, find: (a) the total number of workers. (b) the median class. (c) the lower-quartile class. (d) the number of workers with monthly salary greater than or equal to ₹6,000 but less than ₹10,000.
In the given diagram, O is the centre of the circle. Chord SR produced meets the tangent XTP at P. (a) Prove that △PTR ∼ △PST. (b) Prove that PT² = PR × PS. (c) If PR = 4 cm and PS = 16 cm, find the length of tangent PT.
A hollow sphere of external diameter 10 cm and internal diameter 6 cm is melted and made into a solid right circular cone of height 8 cm. Find the radius of the cone so formed. (Use π = )
A solid wooden capsule consists of a cylindrical block and two hemispheres, as shown. Find the sum of the total surface areas of the three separate parts shown in Figure 2. The radius is 3.5 cm and the cylindrical block is 14 cm long. (Use )
Assertion (A): If sin² A + sin A = 1, then cos⁴ A + cos² A = 1. Reason (R): 1 − sin² A = cos² A. (a) A is true, R is false. (b) A is false, R is true. (c) Both A and R are true, and R is the correct reason for A. (d) Both A and R are true, and R is not the correct reason for A.
A man invested in a company paying 12% dividend on its shares. If the percentage return on his investment is 10%, then the shares are: (a) at par (b) below par (c) above par (d) cannot be determined